ON THE CHANCE OF FREAK WAVES AT SEA

When deep-water surface gravity waves traverse an area with a curved o r otherwise variable current, the current can act analogously to an op tical lens, to focus wave action into a caustic region. In this region , waves of surprisingly large size, alternatively called freak, rogue, or giant waves are produced. We show how this mechanism produces frea k waves at random locations when ocean swell traverses an area of rand om current. When the current has a constant (possibly zero) mean with small random fluctuations, we show that the probability distribution f or the formation of a freak wave is universal, that is, it does not de pend on the statistics of the current, but only on a single distance s cale parameter, provided that this parameter is finite and non-zero. O ur numerical simulations show excellent agreement with the theory, eve n for current standard deviation as large as 1.0 m s(-1). Since many o f these results are derived for arbitrary dispersion relations with ce rtain general properties, they include as a special case previously pu blished work on caustics in geometrical optics.